Conditional Probability

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What is Conditional Probability?

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Conditional Probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads 'the probability of A given B'.

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How is Conditional Probability calculated?

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Conditional Probability is calculated using the formula: P(A|B) = P(A and B) / P(B), where P(A and B) is the joint probability of both events occurring.

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What does P(Male | Full-time) represent?

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P(Male | Full-time) represents the probability that a student is male given that they are a full-time student.

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If P(Studies) = 8/9 and P(Passes and Studies) = 3/5, how do you find P(Passes | Studies)?

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Use the formula: P(Passes | Studies) = P(Passes and Studies) / P(Studies) = (3/5) / (8/9) = 27/40.

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What is the significance of the denominator in Conditional Probability?

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The denominator in Conditional Probability represents the total probability of the condition being true, which normalizes the probability of the event of interest.

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What is the formula for finding P(A | B) when given a contingency table?

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P(A | B) = (Number of outcomes where A and B occur) / (Total number of outcomes where B occurs).

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What does P(Plays Sport | Does Not Play Instrument) indicate?

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P(Plays Sport | Does Not Play Instrument) indicates the probability that a student plays a sport given that they do not play an instrument.

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How do you interpret P(Female | Part-time)?

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P(Female | Part-time) indicates the probability that a student is female given that they are a part-time student.

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What is the relationship between independent events and Conditional Probability?

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For independent events, P(A | B) = P(A), meaning the occurrence of B does not affect the probability of A.

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What is the role of joint probability in Conditional Probability?

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Joint probability, P(A and B), is essential in calculating Conditional Probability as it quantifies the likelihood of both events occurring together.